Classsic harmonic oscilator
a weight on a spring, oscilation is govenred by spring constant K
a weight on a spring, oscilation is govenred by spring constant K
Classsic harmonic oscilator
energy of a quantum oscilator
E_v=hπ(n+12)
E_v=hπ(n+12)
energy of a quantum oscilator
nu(π) for a quantum oscilator
π=(1/2Ο)β(K/ ΞΌ)
π=(1/2Ο)β(K/ ΞΌ)
nu(π) for a quantum oscilator
The reduced mass for quantum oscilation
ΞΌ=(m1m2)/(m1+m2)
ΞΌ=(m1m2)/(m1+m2)
The reduced mass for quantum oscilation
zero point energy for an oscilator
when N is zero our energy is hπ/2
size of quanta for an oscilator
the sepration is always hπ
the sepration is always hπ
size of quanta for an oscilator
How does K affect frequency (π)?
the higher K is, the higher the frequency, and thus the greater the gaps in energy
How do the two masses affect the frequency?
the greater the masses the higher the frequency, and thus the greater the gaps in energy.
converting from normal frequency to wavenumber(π~)
π~=π/c
π~=π/c
converting from normal frequency to wavenumber(π~)
equation for modes of osiclation, where N is the number of particles
3n-6
3n-6
equation for modes of osiclation, where N is the number of particles
Harmonic ocilators scaling to clasical
the points of highest probability cluster to the edges of the oscilation, magichng what we’d expect
the points of highest probability cluster to the edges of the oscilation, magichng what we’d expect
Harmonic ocilators scaling to clasical
